General Relativity Explained in 7 Levels of Difficulty
Vložit
- čas přidán 4. 06. 2024
- Go to nebula.tv/minutephysics to get access to Nebula (where you can watch the extended version of this video), plus you'll get a 20% discount on an annual subscription.
This video covers the General theory of Relativity, developed by Albert Einstein, from basic simple levels (it's gravity, curved space) through to the concepts of how curved spacetime is represented by psuedo-Riemannian manifolds with Lorentzian signature (that is, special relativity and minkowski space are the local tangent space), how matter and energy are represented by an energy-momentum tensor, and how these two together obey the Einstein Field Equations. The solutions to the Einstein Field Equations (including the schwarzschild metric, kerr metric, freedman-lemaitre-robertson-walker metric, etc) represent gravity around massive objects like the sun, earth, and black holes, but also the history and expansion and future evolution of the cosmos. The universe on a large scale is described by general relativity - on a small scale, quantum mechanics. And where they meet... there's still work to be done.
REFERENCES
Wald's textbook - General Relativity
Hartle's textbook - Gravity: An Introduction to Einstein's General Relativity
Carlo Rovelli History of Quantum Gravity: cds.cern.ch/record/442809/fil...
Leon Rosenfeld 1930 paper on quantum gravity: www.edoc.mpg.de/438547
Kerr Metric Solution - en.wikipedia.org/wiki/Eddingt...
Schwarzschild Metric - en.wikipedia.org/wiki/Schwarz...
Eddington-Finkelstein Coordinates - en.wikipedia.org/wiki/Eddingt...
Support MinutePhysics on Patreon! / minutephysics
Link to Patreon Supporters: www.minutephysics.com/supporters/
MinutePhysics is on twitter - @minutephysics
And facebook - / minutephysics
And Google+ (does anyone use this any more?) - bit.ly/qzEwc6
Minute Physics provides an energetic and entertaining view of old and new problems in physics -- all in a minute!
Created by Henry Reich - Věda a technologie
To quote Enrico Fermi: "Having listened to your lecture I am still confused. But on a higher level."
Man, if that quote doesn't describe my 400 level physics classes so well.
This captures my feeling precisely.
That's pretty much all learning though, just increasing the level you're confused at until you're the most confused one in the world
@@portobellomushroom5764 At that point, you're so confused that the only way for you to be not confused is to make new discoveries in your field.
@@YoshisaurUnderscore I think you mean the only way to be confused in new and interesting ways is to make new discoveries in your field.
You know it's going to get serious when you're on 7 and the video is only half over
Though, most of the latter part is sponsor fluffing these days anyways, so, it's not really that more serious.
Or... there are a lot of ads.
not to mention he was like "ima speak a little slower now"
It got serious for me at stage 4. I get inertia, I get the whole 'ball in the middle of a sheet' example, and I get that time is a series of snap shots, but WHY any of that stuff happens is totally beyond me.
Hunter Humphrey
Serious = good in this case.
"general relativity is a physics theory created by Albert Einstein"
Me: hold on smart guy, take it easy.
I must agree.
Gui
Let's start simpler...
a squared plus b squared equals c-squared.
@@ivoryas1696 woah there, shapes? i thought this was physics
@@fynexjeralt4186
Lmao, that's low-key how I felt entering Pre-calc 😂🤔😐
Hahahahahahahahahahaha 😂
Trying to explain relativity to me
In 7 levels
In 6 minute video
At 5 in the morning
In 4 walled room
In 3 dimensional world
On 2 dimensional screen
And in 1 dimensional BRAIN
NICE TRY👍
*In 4 dimensional world
@@TheBlueWizzrobe 3d +1 world
With 0% knowledge of nothing
@@nothing9220 no knowledge of nothing = knowledge of everything = infinity
sounds great!
p
0:06 : What you study in class
1:53 : What you get for homework
4:30 : The exam
I can certify your comment. Its accurate
"You went over it briefly 3 years ago, so now in this class we only review it"
This is, indeed, correct.
This comment has to be pinned 😂
Its in the small text on the side that they never tell you to read or acknowledge at all in my experience
7 levels, in 6 minutes. Less than a minute per level. Truly living up to the name “minutephysics”
That's cool but also level 7 was about half of the video (2:58)
jan Melantu
"It's what I do."
3:20 is my favorite part because I love how he lists off the numerous observations that validate the model. It's the observations that make this a physics theory instead of just mathematics.
2:22 "Oh that isn't too bad"
2:24 "Oh it's actually 10 equations, ok"
2:25 "Oh god oh f*ck"
Even the 2:25 is still the shortened form...
hahaha man best comment ever
10 non-linear partial differential equations, I mean, good luck man
Thanks for recommending Vitamania Henry!
Sup my brotha 😂
BRO I LOVE YOU TWO GUYS
The check mark looks so suspicious I was about to report this account
Hey Derek, would you like to make a video explaining the differences between making curiositystream, CZcams originals and casual veritasium videos
I was here
my two brain cells have been stuck on level 2 since past 5 years
Lol You'll get it.
@@anoushka6439 Oh, lah-di-dah, look at you with your extra smart brain cell that can do twice the work of normal brain cells.
man! you got the same image as mine!
yes
i am a kid
My brain cell went "kablooy" 🤯
glad rest of them made it through
I've been studying this for years. This is by far one of the most accurate videos on the field. Level seven is the strict construction of the equations and their solution throughout classical differential geometry, tensor calculus, complex analysis, linear algebra, ordinary differential equations, partial differential equations and special functions among the classical fields.
This is simply a compendium of what this is in its entirety. This is the field of Riemann Manifolds.
It is so confusing that me, my future and past self gathered together yet couldn't understand anything
🤣😂same 😅
The image of the black hole was not from the center of the Milky Way but rather from data collected observing the galaxy M87.
I came here to say this.
I came here to say exactly that... #copypaste
"One of the largest known supermassive black holes, M87* is located at the center of the gargantuan elliptical galaxy Messier 87, or M87, 53 million light-years (318 quintillion miles) away."
Sagitarrius A* is the one in the middle of the Milky Way, it is about 20,000 light years away, but obscured by all the dust in between.
Also was going to say this. Worth nothing that GR has been tested by other groups using the orbits of stars around Sagittarius A*
He corrected that in the video. 3:42
I made the same mistake myself when mentioning the 2020 nobel prize in physics and the 2019 photographed black hole
The time I spent watching pbs spacetime did not goes to waste. I manage to nod at the explanation up to level 3. 🎉🎉🎉
I felt that.
@Charles Clarke bruh that's literally just a full course on GR
@Charles Clarke actually I do know about the ScienceClic YT channel, and yeah it's great! Just the perfect level for me
Omg I love spacetime! I didn’t realize it was so popular
I understand Level 6.5 stuff.
But wait...THERE'S MORE!
That's why I love physics!
3:42 That's not the black hole at the centre of the Milkyway. It literally says M87 on the picture!
YEP. Came looking for this comment.
(Tho MinutePhysics still does a great job!)
"Further reading":
M87* is the SMBH at the middle of the Virgo A galaxy (a.k.a. M87). Our own SMBH in the Milky Way is Sagittarius A*. And the "star" part is important to the name - one does not simply leave it off.
@@Alpinwolf5 so does that mean you do agree with me
@@dreadnoughtus2598 yeah, totally! I only added more detail for other passing readers. :)
@@Alpinwolf5 thanks for your support in this matter. It is greatly appreciated.
@@connorgolsong290 which was.......?
Words cannot express your talent and I'm so grateful. Thank you for all these insights and inspiration. It took me ~1000 hours to produce 17 hours of video explaining Special Relativity in just 3 levels of complexity …
This is the kind of stuff that originally bothered me about science: that you have to keep coming back to a topic in order to learn the next stage as your level of understanding increased. Now, as a biology teacher, it is one of the things that makes science, and learning in general, fun. "Remember how you learned in middle school that plants make energy from sunlight? Well it's actually more complicated than that." "Remember how you learned in high school that plants make monosaccharides from sunlight? Well it's actually more complicated than that."
I take the view that this is because everything in science is an approximation. The approximations get more accurate, Newtonian gravity, general relativity, whatever quantum gravity might be, etc. but they never become statements about the state of being of nature. Only nature itself a knows how nature is. And science merely concerns what we can say about nature.
@@Cosmalano completely agree with your statement about us never knowing the absolute truth/ exact way something works. Personally, I would switch "nature" for "God" but to each their own.
@@adnanchinisi7871 God? lol
@@tattwa1 Aw c'mon. God is just the standard thing we stuff in all the gaps of our knowledge. Each time we learn something new, we yank the god out of that gap and stuff it into the next.
@@Cosmalano This is also one of the core tenets of Kants philosophy.
en.wikipedia.org/wiki/Transcendental_idealism
Level -1: falling Apple + head = ouch.
Newton level: fallin apple + head = gravitational universal law
@@Epilogue_04 Oh, what's Steven hawking Level then?
I like this level. And I'm hungry.
Lol
Level -1.5
ground = good
Not ground = ouch
This is a brilliant idea! To present such an advanced subject in different levels next to each other, it really makes it easier to follow
This was SOOOOOO good!
Hearing all the explanation after one another really helped me to understand it!
It's also kind of funny when you realise that level 1-6 is only the first half of the video XD.
Level 14 of General Relativity: Obtaining a PhD in Theoretical Physics
Not neccesarily. Anyone with a class in GR can understand most of it. PhD in Theoretical Physics is much more sophisticated it develops on already developed GR and Quantum fields theory for example trying to develop parts of string theory.
I have a theoretical degree in physics
@@qazwerty41339 I have a physics in theoretical degree.
Nicee
@@denverbeek I have theoretical in degree physics
Level 3: Okay, kinda get the main idea
Level 4: ｗｈａｔ
Not liked because number 69 likes
really
@@user-rc8bb7yb1e dude you have a cool name
Just ignore the word salad and listen to the stuff he says after that, it makes more sense; I feel he shouldn't have led with the proper scientific name
@@dsdy1205 Ikr but now I can show off to everyone by knowledge of a pseudo-riemannian manifold is
I have been trying to understand it for a long time and this video put everything that I have found in a correct order and now I finally did understand it. AMAZING
I like that you include geodesics, a major step in my learning.
The algorithm has not been kind to your channel, this is the first of your videos that has popped up for me in probably a year.
@Pinco Palla yep that explains many things
Understanding you tube algorithms in 7 steps....
.
.
.
.
.
.
.
NO CHANCE
@@leeroy265 TRENDING
Then subscribe, and get all the notifications. Win-win, for you and henry.
I'm level 7 for things that I know.
I'm level 0 for things that I understand.
Ricci tensors, curvature scalars, antisymmetric tensor fields, Grassmann variables, Christoffel coefficients, diffeomorphism invariance, isotropic pressure in vacuum states with cosmological energy densities, nonlinearity distinguishment from e.g. Schrodinger's equation and Levi-Civita symbols.
Is it weird that I'm the exact opposite: Level 0 for things that I know; Level 7 for things that I understand?
@@TheShamansQuestion He wants to understand the things which he doesn't understand while neglecting the others.
You want to understand the things you already understand but in as much more depth as possible while neglecting others..
@@srajanverma9064 very nice 👌🏻 you're right my want is there but I'd de-emphasise "want" and say it's more once I get knowledge, I can understand it deeply (and because I want to/go for depth), plus a sceptical, Socratic element of "I know that I know nothing" (but that is probably more relevant to "understanding" in this case, so might be wrong on that)
You just summed up physics
I have just discovered your vids and they are unreal! The fast pace really suits hows racy my minds works its great 😁👍
Cool concept for a video. I especially enjoyed the "level 1 again" explanation of people's personal experience of gravity on earth in terms of your GR explanation.
and here I am trying to pretend that I understand
I j ow you’re joking but understanding is the easy part. The mathematics behind it is the hard parts, but as with anything practice makes perfect.
You don't invent a theory, do you?
Fake it until you make it
And here i am, trying to pretend that i relate to you.
this video makes you feel like it is explaining something, that you are just not getting. It is not honest in this matter. You're not supposed to understand what a Riemannian manifold is by hearing the term, don't feel bad about it.
Having solved the Einstein Field Equations for a physics final in college, fuck. That is all.
what topics do you go over before learning about Einstein's field equations?
@@abelnolan9378 differential geometry and differential equations, I believe
@@abelnolan9378 differential geometry, you will need tensors too, and a bit of classical mechanics and differential equations
It takes at least a few hours to derive even the simplest solution (Schwarzschild solution) to the EFE by hand. A set of 10 highly coupled nonlinear differential equations makes even the most brilliant mathematicians cringe.
I once had a professor that said "Everyone should curl up with a warm drink and spend an evening deriving the Einstein Tensor for the FLRW metric by hand at some point in their life". Needless to say, I haven't done that yet.
Danke schön Henry für dieses toll und sehr verständlich erklärtes Video... 👍👍.... Macht so weiter.... 👍
Really nice explanation of the equivalence principle and just a nice conceptual summary of GR.
Okay, time to change my LinkedIn description to “Physicist specialized in General Relativity”
same, I changed it to, "having a theoretical degree in physics"
Here I am finishing my Master Thesis on a Loop Quantum Gravity topic and trying to write a nice overview of what have brought us this far. This video is so perfect now I want to put the link to it in my thesis instead of writing chapter 1.
Great work.
Hey I have some doubts about lqg . Can I ask you ?
@@kamakaze5448 Sure :)
It’s been two years since this comment, but I’m curious to hear more from someone who has worked under a master’s program. To be frank, I’m a mathematician so sometimes I jump to the mathematical properties of these theories rather then the physical. Having glossed over a few papers on LQG, my sense is that the quantization of space challenges the Reimannian geometry of GR in a controversial way? At the end of the day, these theories come down to their predictive qualities (last I heard there were promising but inconclusive findings from gamma-ray bursts)… what’s the story on LQG today? Is it still alive and kicking?
I leave this comment because I wanna hear his response
Nobody literally nobody:
1st year Physics Undergraduates:I'm gonna unite GR&QM
I'm also a first year physics UG currently at hansraj college. Delhi university
Which college you are from
@Swastik Majumder nice! I also want to get into an IISER. I am going to give the entrance exam this year (again, as I didn't clear it last year), and I hope to get into an IISER!
@@yashkrishnatery9082 what are you studying there?
@@pulkitmohta8964 I'm preparing for JEE
Last year I qualified both exams but didn't took admission as I didn't got rank under 2000
I didn't took any formal coaching last time so I dropped and preparing
@@pulkitmohta8964 at hansraj I'm studying nothing. I'm just focusing on JEE. I just took admission there as I was getting in almost all DU colleges
This is a fantastic video, and a very effective and engaging style of presenting it. Bravo!
3:42 The image is of the black hole at the centre of M87, not the Milky Way, hence the picture being labelled M87* instead of Sagittarius A*
I think they tried imaging it too but there's a bunch of junk in the way and they're about the same angular size so yea.
Came to the comments looking for this, glad I'm not the only one who noticed that it's M87 and not Sagittarius A star
This is the ultimate video to confuse flat-earthers even more :-D
and round-earthers too
I had a discussion with a friend who's into conspiracy stuff, for shits and giggles mostly mind you, about how in a very special way, yes, you can say that the earth is flat.
Twas a fun talk haha
No. Flat earthers are immune to facts.
You thought the *Earth* is flat?! Well guess what, even space and time aren't flat!
still stomping on those ants? lol
This the BEST video I've watched about General Relativity!!
This totally helped me understand. Great concept.
Remember when math and physics had numbers?
.... yeah me neither
indices !
I'm firmly convinced taking a maths/physics course is about the most roundabout way of learning the greek alphabet.
I think I saw an 8 somewhere in the video, but it might have been an illusion
@@FranciT98 Hey, you do learn it pretty quickly.
Non-mathematicians: wait, it's not about the numbers?
Me: never has been (points gun)
I am very glad he mentioned that GR is incomplete
I guess that should still not be the main take away from the video.
When you're one of the most successful theories in the history of physics, but people only mention you to explain how you can't answer questions you weren't made to answer.
It baffles me that educators always do that when they talk about GR (but not as much with Quantum Mechanics). 99.99% of the people don't know these theories when they do apply. Why are we so fixed on the cases they don't apply?
Edit: I'm not saying to ignore the gap in our therories or that it is not important or interesting. I just meant to say that when first learning about relativity it's no use focusing TOO much of your attention there from the beggining.
It's a great goal to work towards solving those mysteries. But realistically, you can't do much before you learn GR properly. Be informed about it and use it as a motivation to learn GR. You'll get there when you get there. And if you're already there, you're awsome! ;D
@@ngiorgos When I hear that quantum mechanics and GR still need more work to make the 2 compatible, I feel excited. It tells me that there is more to discover. It helps teach that science is in fluctuation. It changes and improves. There are questions left to solve and WE could be the ones to solve it.
@@ngiorgos every scientific theory from over 200ish years ago has been proven wrong one by one, our current theories are more right in more circumstances, but they're still wrong. In another 200 years we'll look back on some of this stuff the way we do phlogiston or the luminous aether. General relativity is the best tool we have to understand spacetime, but it'll be replaced eventually by something even more accurate!!
anyone else think this was Music is Win?
the earth surface analogy was awesome. great work!
simple yet complex, great work
3:44 That is NOT "the black hole at the center of the Milky Way" (Sagittarius A*) that is the black hole at the center of galaxy M87. They did consider imaging Sagittarius A*, but that was ultimately not their target. Edit: It turns out I do not know how to spell "Sagittarius."
That’s what you got out of this?
@@GrayLynch No, that is a correction to a mistake they made in the video. In no way did I suggest that the video wasn't worth watching or is otherwise "ruined" as a result of their mistake; but if it were me and I made a mistake in a science education video, I would hope I would be corrected.
I immediately noticed that error as well.
Yeah but fan fuct: we do orbit the M87 black hole
@@alwaysdisputin9930 have you got a source on that?
1:20 that's a nice globe you got there.
Me, an intellectual: actually, it's a pseudo-Riemannian manifold with Lorentzian signature,... But thank you! 😊
..out of all of them......this made me laugh the most. Well done 😂
Nondegenerate symmetric metric tensor too. Establish the linear connection/Levi-Civita connection with use of Weyl spinors (helicity operators).
Dave P
_IQ +10_
I love how equivalence principle is added in the subtitles.
YAAAY do this more please! Great content
the funny thing is, he's only explaining it for those who already know.
I wish it was possible to explain it for the ones who didn't know. I wish that every day
Skatheo
Well beyond around level 4, yeah, but it's seems pretty okay otherwise.
@@ngiorgos I think Vsauce's "Which way is down" video does a pretty good job. It gets more obtuse near the end and doesn't even get as high-level as this, but I like it a lot.
@@TheBlueWizzrobe Yes, I loved that! And Veritasium's video "why gravity is not a force" is also an excellent presentation.
But the best they can do is give an overview of the theory and some intuitive explanations. The maths are still untouchable, unfortunately.
I got to around level 5, then level 6 I only knew some of it.
So good. I've tried so many times to explain the way the ground pushes you away from a straight line and I've never once passed understanding across. Now I can link to this video with the clear diagram, and maybe in future, I'll succeed in showing the beauty of this idea to others.
SOOOOOOOOO BEAUTIFUL..! thanks man.. Best explaining ever ♥
Wow. This was great. Thank You 🙏
Thanks for summing all that up in a short video. I've seen a lot of videos explaining GR/SR on different "levels" and this gives me a nice feel on where I stand in my understanding of the subject.
👀
👀
👀
👀
👀
👀
Wow! This is great. Thank you!
Amazing explanation, thank you.
The video hasn’t started yet and I’m already confused.
That's why there's this video! czcams.com/video/wrwgIjBUYVc/video.html
Just picture space-time as water flowing towards a drain that is moving on the seabed below.
Now picture the water as rainbow colors that never mix together (stripes maybe) as they flow towards the drain.
Now picture the drain as a sphere. The 2D nature of its opening is the diameter and the edge is the equator.
Now put a leaf anywhere in or on the water, near or far. What happens to the leaf in the different places you put it?
That is space-time... with one exception...
A drain sends the water somewhere else whereas space-time is fixed in place so it doesn't go anywhere. Space-time is literally pulled inward (or rather pinched) by the mass of a planet, star or blackhole as they move through it and it unpinches the farther away it gets from point A while heading to point B.
Like walking on a memory foam mattress with stuff all over it. Your feet are the mass and the mattress is space-time and the stuff falls towards your feet depending on where you are on the bed.
Great video. Your videos got me interested in general relativity six years ago, and to this day I’m still trying to become a mathematical physicist so I can study quantum gravity. ❤️
This is actually the best summary video I've ever seen on physics.
You are so blessed to understand these things.
Wow that was very quick but so educational! Thanks so much!
It's not a question of "when? " my dear Reggie, but "where?"
It's the same thing with the concept of spacetime
No no both when n where n how much
It’s about whenere/ wheren.
Metaphysics: it's not a question of "what?" my dear Reggie, but "why?"
Level 90:
Discovering a mathematical notation that encapsulates both General relativity and Quantum mechanics and winning the nobel prize
I've been a Nebula subscriber for at least a year and I've never seen Minutephysics mentioned on the site under you said to go looking for it.
"very high level stuff" - like nobody has figured out how to do it yet
I have been subscribed to this channel for quite some time now, I initially got interested because of my great physics teacher in high school. Back then I did not understand most of the videos at a deeper level (so the primary target audience).
After 3 1/2 years of studying physics, I have my GR exam on monday and can happily say: I knew everything in this video! And it makes me glad to finally be at a point where I do understand this stuff at a deeper level. It took quite some time, but I got there.
Of course I am still just beginning to be a physicist and there is MUCH I don't know yet and MUCH and I don't know that I don't know yet. And I am excited and looking forward to finding it out!
Keep it up and thanks for your service to science :D
Same story here.
Such Videos brought me to physics. According to plan, I'll have my Bachelor in half a year.
@@fischmann1746 Then I wish you best of luck for your thesis! Do you already know in what area you will write it?
@@aemmelpear5788
Thanks.
I'll write a program that simulates a non-linear mechanical system and analyse it's behaviour. What system in precise isn't clear yet.
Writing simulations in non-linear physics is pretty much the profession I want to finde myself in some day.
@@fischmann1746 Sounds great! Computational Physics is also one of my favorite areas!
I went into this video thinking, oh, that's cool, he'll explain it in incrementally more complicated ways so I'll be able to understand it by the end!
Me at difficulty 2: huh
Just finished taking general relativity this quarter that passed, and I can honestly say that this is the hardest topic I've seen so far in my physics career, but also the most enjoyable.
This video: There are 7 levels of understanding gravity.
Me: I can make it to level three, take it or leave it.
DW thats pretty good
i'm gonna start calling the 90s the "nowdays"
I don't get it.
@@kennarajora6532 .
@@kennarajora6532 check the graph at 4:46
@@metametodo oh alright, thanks.
You got a too short of a time scale if you don't think of it as nowadays.
im new this channel is awesome! lots more ppl would love to learn about physics but we need more stuff like this I feel like when ppl don't think physics r cool it's might b bc they're not getting an explanation that's ez to understand
Awesome approach!
Videos like this remind me of why I love physics.
M87 is not at the center of the Milky Way! It’s in another galaxy about 50 million lightyears away.
This is amazing. I love seeing high level knowledge explained quick. I’ve had this idea for a while about predicting the future with all the variables of today. Ultimately it comes back the is anything actually random and to that quantum mechanics says yes
yeah.. this is something I definitely have to research more for a better understanding
Today we have a Rover landing and minute physics uploaded, blessed day
Truely.
Loved the level 0, something Einstein did 😂😂
Ricci tensors, curvature scalars, antisymmetric tensor fields, Grassmann variables, Christoffel coefficients, diffeomorphism invariance, isotropic pressure in vacuum states with cosmological energy densities, pseudo-Riemannian manifolds, nonlinearity distinguishment from e.g. Schrodinger's equation and Levi-Civita symbols.
Thank you for described level by level.
Thanks for the video.
4:02 what a great explanation of gravity!:)
4:48 'Nowadays' ends at 1997, wonder when the next breakthrough will b e
@@qingyuewu6429 It's a bot
You know what the insanely insane (and awesome) part of this video this? THERE'S MORE LEVELS!
(For reference, I think I'm at 6.5, or at least between that and level 7. The idea of manifolds and tensors is something I have yet to understand, but I understood the rest of Level 7).
Thanks for subtitles
What is General Relativity?
Level 0 answer: "posts this youtube link"
the best gr guide on CZcams
I love your videos! Please communicate to nebula creators that we NEED to be able to play videos at 2+x speed. I would spend so much more time there if I wasn't able to watch twice as much here in the same time.
another great video!
I literally have to do a research paper on general relativity, thanks so much.
First of all very good video you have made here!!! Great.
Secondly i would like to make a correction that the image of the blackhole is not that of the blackhole at center of milky way but is that of blackhole at center of M87.
This is great. Thank you
Till this day i still dont understand
Riemannian manifolds are on the syllabus for my differential geometry course, so hopefully I gain a better appreciation for this video in three months
The best of luck! Just be aware of the difference between Lorentzian and Riemannian manifolds. Riemannian manifolds are locally Euclidean spaces. Lorentzian manifolds are locally Minkowski spaces
let us know in 3 months and tag us. keen to hear it from someone active going through the process
Now did you get it?
05:09 „It is very high-level stuff“
Our math teacher when creating the tests: „Haha what did you say? Pathetic.“
I like your quotation marks
@@wellshit9489 I'm Russian so it explains everything
@@deadoira I wasn't being sarcastic dw, we have them in Iceland where I live too
@@wellshit9489 I know, just decided to explain :)
Beautiful!!.
beautiful explanation
Finally, I knew taking a course in differential geometry would be useful someday.
Can u do a general relativity series just like special relativity but like longer? Please?
general relativity is really another level, but if you think that you have a good understanding in special relativity, the PBS Space Time has a playlist "Curved Spacetime and Gravity" or something like that, its really good
czcams.com/play/PLsPUh22kYmNAmjsHke4pd8S9z6m_hVRur.html
Thx
I love the jazz music stops vibe given by having jazz music literally stopping
4:05 I finally understand how gravity works on our planet. Omg. That was the best explanation I’ve ever seen.
I'm at an approximate 2.5, if I had to quantify it, and when I talk about this to people in lower levels, they feel like I'm a genius, even tho I tell them I basically know nothing. It's wild how the depth of knowledge is so overwhelming that even a slight amount of it can make you look way smarter than you actually are to people who just used their time learning other things.
Yeah, same with me. I hate appreciations. Whenever I tell people about such things, they start feeling like I'm a genius. But it feels strange and Little bit funny when most people don't know about the reality ( i mean the beauty of maths and physics) . Why most of people do boring jobs and why they want to become rich? We will die at the end so do some interesting.
I don't want to live a normal life😅 but my parents are forcing (a little bit) to do some government job or any job.
Sharing my thoughts with others feels good :)
Having conversations you wouldn't normally have can really help to put some things into perspective.